ER 9 CORRELATION AND REGRESSION Using and Interpreting Concepts DEXE Finding the Equation of a Regression Line In Exercises 13-22, find the equation of the regression line for the given data. Then construct a scatter plot of the data and draw the regression line. (Each pair of variables has a significant correlation.) Then use the regression equation to predict the value of y for each of the given x-values, if meaningful. If the x-value is not meaningful to predict the value of y, explain why not. If convenient, use technology to solve the problem. 13. Miami Building Heights The heights (in feet) and the number of stories of nine notable buildings in Miami (Source: Emporis Buildings) 492 484 450 430 410 Height, .r 764 625 520 510 Stories, y 55 47 51 28 39 34 33 31 40 (a) x = 500 feet (b) x = 650 feet (c) x = 310 feet (d) x = 725 feet 14. Age and Vocabulary The ages (in years) of seven children and the number of words in their vocabulary Age, .r 3 4 4 5 6 2 3 Vocabulary size, y 1100 1300 1500 2100 2600 460 1200 (a) x = 2 years (c) x = 6 years (b) x = 3 years (d) x = 12 years 01223 SECTION 9.2 LINEAR REGRESSION 517 EXERCISES Extra Help atLab (d) (b) Building Basic Skills and Vocabulary In Exercises 1-8, match the description in the left column with a description in the right column. 1. Regression line 2. Residual 3. The y-value of a data point corresponding to xi 4. The y-value for a point on the regression line corresponding to Xi 5. Slope 6. y-intercept 7. The mean of the y-values 8. The point a regression line always passes through a. The difference between the observed y-value of a data point and the predicted y-value on the line for the same data point b. i c. The line of best fit d. Yi e. b f. (x, y) g. m h. y Graphical Analysis In Exercises 9-12, match the regression equation with the appropriate graph. (Note that the x- and y-axes are broken.) 9. = 1.04x + 50.3 10. = 1.662x + 83.34 11. = 0.00114x + 2.53 12. = -0.667x + 52.6 a. Energy-efficiency rating =1 11 10 10 9 8 y C. y 18 17 Fat (in grams) 14 654321 16 15 6100 6300 6500 Cooling capacity (in BTUs) 11 32 33 34 35 36 37 38 Protein (in grams) b. d. Systolic blood pressure y 225 200 175 150 125 100 75 EVITTTTTT * 15 25 35 45 55 65 75 Age (in years) Leisure time (in hours per week) y 28 26 24 22 20 18 40 42 44 46 48 50 52 Work time (in hours per week)